EC GATE 15 Paper 02 New2

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1

General Aptitude

Q. No. 1 – 5 Carry One Mark Each

1. What is the adverb for the given word below?

Misogynous(A) Misogynousness (B) Misogynity

(C) Misogynously (D) Misogynous

Answer: (C)

2. Choose the appropriate word – phrase out of the four options given below, to complete the

following sentence

Dhoni, as well as the other team members of Indian team _______________ present on theoccasion

(A) Were (B) Was (C) Has (D) Have

Answer: (B)

3. Ram and Ramesh appeared in an interview for two vacancies in the same department. The probability of Ram’s selection is 1/6 and that of Ramesh is 1/8. What is the probability thatonly one of them will be selected?

(A) 47/48 (B) 1/4 (C) 13/48 (D) 35/48

Answer: (B)

Exp: 1 1P Ram ; p Ramesh6 8

0 am7 1 51 p only at p Ram p not ramesh p Ramesh p n R

6 8 8 6

12 1440

4. Choose he word most similar in meaning to the given word:

Awkward

(A) Inept (B) Graceful (C) Suitable (D) Dreadful

Answer: (A)

5. An electric bus has onboard instruments that report the total electricity consumed since thestart of the trip as well as the total distance covered. During a single day of operation, the bustravels on stretches M, N, O and P, in that order. The cumulative distances traveled and the

corresponding electricity consumption are shown in the Table below

Stretch Cumulative distance (km) Electricity used (kWh)

M 20 12 N 45 25

O 75 45

P 100 57

The stretch where the electricity consumption per km is minimum is

(A) M (B) N (C) O (D) P


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2

Answer: (B)

Exp:

Stretch Comulative

distance(km)

Electricity

used

(kWh)

Individual(km)

Distance

Individual

electricity(kWh)

M 20 12 20 12

N 45 25 25 13

O 75 45 30 20

P 100 57 25 12

For 12M 0.620

13 N 0.55525

20O 0.66730

12P 0.4825

Q. No. 6 – 10 Carry Two Marks Each

6. Given below are two statements followed by two conclusions. Assuming these statements to be true, decide which one logically follows.

Statements:

I. All film stars are playback singers.

II. All film directors are film stars

Conclusions:

I. All film directors are playback singers.

II. Some film stars are film directors.

(A) Only conclusion I follows (B) Only conclusion II follows

(C) Neither conclusion I nor II follows (D) Both conclusions I and II follow

Answer: (D)

7. Lamenting the gradual sidelining of the arts ill school curricula, a group of prominent artistswrote to the Chief Minister last year, asking him to allocate rnore funds to support arts

education in schools. However, no such increase has been announced in this year ’s Budget.The artists expressed their deep anguish at their request not being approved, but many of themremain optimistic about funding in the future

Which of the staternent(s) below is/are logically valid and can be inferred from the abovestatements?

(i) The artists expected funding for the arts to increase this year

(ii) The Chief Minister was receptive to the idea of increasing funding for the arts


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3

(iii) The Chief Minister is a prominent artist

(iv) Schools are giving less importance to arts education nowadays

(A) (iii) and (iv) (B) (i) and (iv) (C) (i), (ii) and (iv) (D) (i) and (iii)

Answer: (B)

8. A tiger is 50 leaps of its own behind a deer. The tiger takes 5 leaps per minute to the deer ’s 4.If the tiger and the deer cover 8 metre and 5 metre per leap respectively. What distance inmetres will be tiger have to run before it catches the deer?

Answer: 800

Exp: Tiger 1leap 8 meter

Speed 5leap hr 40m min

Deer 1leap 5meter

speed 4hr 20m min

Let at time ‘t’ the tiger catches the deer.

Distance travelled by deer + initial distance between them50 8 400m = distance covered by tiger.

40 t 400 20t

400t 20 min

200

total distance 400 20 t 800 ms

9. If 2 2 2a b c 1, then ab bc ac lies in the interval

(A) [1, 2/3] (B) [ – 1/2, 1] (C) [ – 1, 1/2] (D) [2, – 4]

Answer: (B)

10. In the following sentence certain parts are underlined and marked P, Q and R. One of the parts may contain certain error or may not be acceptable in standard written communication.Select the part containing an error. Choose D as your answer if there is no error.

The student corrected all the errors that the instructor marked on the answer book

P Q R

(A) P (B) Q (C) R (D) No error

Answer: (B)

Exp: The is not required in ‘Q’


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4

Electronics and Communication Engineering

Q. No. 1 – 25 Carry One Mark Each

1. Let the signal f t 0 outside the interval 1 2 1 2T ,T , where T and T are finite. Furthermore,

f t . The region of convergence (RoC) of the signal’s bilateral Laplace transform F(s)

is

1. A parallel strip containing the j axis

2. A parallel strip not containing the j axis

3. The entire s – plane

4. A half plane containing the j axis

(A) 1 (B) 2 (C) 3 (D) 4

Answer: (C)

Exp: For a finite duration time domain signal ROC is entire s-plane.

2. A unity negative feedback system has an open – loop transfer function

K G s

s s 10

. The

gain K for the system to have a damping ratio of 0.25 is ______________.

Answer: 400

Exp:2

k G(s)

s 10s

2

2

n

n

2

k

CLTF s 10s k

0.25

k

k

100.25

2 k

10k

0.5

k (20)

k 400


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5

3. A mod – n counter using a synchronous binary up – counter with synchronous clear input isshown in the figure. The value of n is _____________________

Answer: 6

Exp: To find the modulus of the counter, consider the status of the inputs (QB, QC) as 1.

So, A B C DQ Q Q Q 0110

So, it is a MOD-6 counter

4. By performing cascading and/or summing/differencing operations using transfer function blocks 1 2G s and G s , one CANNOT realize a transfer function of the form

(A) 1 2G s G s (B)

1

2

G s

G s

(C)

1 21

1G s G s

G s

(D)

1 2

1

1G s G s

G s

Answer: (B)

5. The electric field of a uniform plane electromagnetic wave is

7x yE a j4a exp j 2 10 t 0.2z

The polarization of the wave is

(A) Right handed circular (B) Right handed elliptical

(C) Left handed circular (D) Left handed elliptical

Answer: (D)

Exp:

7 j 2 10 t 0.2z

x y

z

y

E a 4 ja e

E cos t

E 4cos 2 4sin t

So, it left hand elliptical polrization

7

2 10

0.2

4 Bit BinaryCounter

CLK CLOCK

AQ

BQ

CQ

DQ

CLEAR

AQ

BQ

CQ

DQ


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6

6. A piece of silicon is doped uniformly with phosphorous with a doping concentration of16 310 / cm . The expected value of mobility versus doping concentration for silicon assuming

full dopant ionization is shown below. The charge of an electron is 191.6 10 C. The

conductivity 1in S cm of the silicon sample at 300 K is _________________

Answer: 1.92

Exp: As per the graph mobility of electrons at the concentration 1016/cm3 is2cm

1200V s

So,

2

n cm1200V s

N D n

16 19

1

N q

10 1.6 10 1200

1.92S cm

7. In the figure shown, the output Y is required to be Y AB CD . The gates G1 and G2 must be, respectively,

(A) NOR, OR (B) OR, NAND (C) NAND, OR (D) AND, NAND

G1

G2

A

B

CD

Y

1.E 13 1.E 14 1.E 15 1.E 16 1.E 17 1.E 18 1.E 19 1.E 20

1400

1200

1000

800

400

0

200

600

Electron Hole

Hole and Electron Mobility in Silicon at 300 K

M

o b i l i t y ( c m

2 . V - 1 . s - 1 )

3Doping concentration cm


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7

Answer: (A)

Exp: Given expression is Y AB CD

The first term can be obtained by considering 1G as NOR gate, and second term CD isobtained from another lower NOR-Gate. So, final expression can be implemented by

considering G2 as OR-Gate.

8. In the bistable circuit shown, the ideal opamp has saturation level of 5V . The value of

1R in k that gives a hysteresis width of 500 mV is ______________.

Answer: 1

Exp:

TH TL

1 1

2 2

Hysteresis V V

R R L L

R R

1 1

1

R R 500mV ( 5) 5

20k 20k

R

2k

1R

2R 20k

inv

outv

0V

TLV THV

L

L

IV


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8

3 3

1R 500 2 10 10

1000 1k

9. Two causal discrete – time signal n

m 0x n and y n are related as y n x m

It the z – transform of

22

y n is , the value of x 2 is __________ z z 1

Answer: 0

Exp: n

m 0

y n x m

According to accumulation property of z-transform

1

2 3

1

X z z X z2Y z

z z 1 z 11 z

2z 2zX zz 1 1 z

x n 2u n 3 thus x 2 0

10. The bilateral Laplace transform of a function 1 if a t b

f t0 otherwise

(A)a b

s

(B)

2e a b

s

(C)

as bse e

s

(D)

s a be

s

Answer: (C)

Exp: Given 1 a t b

f t0 otherwise

st

0

ast st st

0 a b

L f t e f t dt

e f t e f t dt e f t dt

bst

a

st bs as

as bs

0 e dt 0

be 1

e eas s

e e

s


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9

11. The 2 – port admittance matrix of the circuit shown is given by

(A)0.3 0.2

0.2 0.3

(B)15 5

5 15

(C)3.33 5

5 3.33

(D)0.3 0.4

0.4 0.3

Answer:

Exp: Correct answer not given in options

0.3 0.2

0.2 0.3

12. The value of x for which all the eigen – values of the matrix given below are real is

10 5 j 4

x 20 2

4 2 10

(A) 5 + j (B) 5 – j (C) 1 – 5j (D) 1+ 5 j

Answer: (B)

Exp: Let

10 5 J 4

A x 20 2

4 2 10

Given that all eigen values of A are real.

T

A is Hermitian

A A ie. A A

10 x 4 10 5 j 4

5 j 20 2 x 20 2 x 5 j

4 2 10 4 2 10

13. The signal cos 10 t4

is ideally sampled at a sampling frequency of 15 Hz. The sampled

signal is passed through a filter with impulse response sin t

cos 40 t

t 2

. The filter

output is

(A)15

cos 40 t2 4

(B) sin t15

cos 10 t2 t 4

(C)15

cos 10 t2 4

(D) sin t15

cos 40 t2 t 2

5

10 10


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10

Answer: (A)

Exp: Given signal is x t cos 10 t4

Neglect the phase-shift4

and it can be inserted at the end result.

L1 11

If x t cos 10 t X f f 5 f 52

Given filter impulse response is,

sin th t cos 40 t

t 2

sin c t sin 40 t

1H f rect f * f 20 f 20

2 j

1 rect f 20 rect f 202 j

1X f repeats with a value of 15Hz and each impulse value is15

2

Thus the sampled signal spectrum and the spectrum of the filter are as follows:

s

r

15X f H f f 20 f 20

4 j

15x t sin 40 t recovered signal

215

= cos 40 t2 2

Insert the neglected phase shift4

20 15 10 5 5 10 15 20

sX f 15/ 2

f H(f

20

20

H f


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11

r 15 15

x t cos 40 t cos 40 t2 2 4 2 4

14. A sinusoidal signal of amplitude A is quantized by a uniform quantizer Assume that the signalutilizes all the representation levels of the quantizer. If the signal to quantization noise ratio is

31.8 dB, the number of levels in the quantizer is ____________________Answer: 32

Exp: 2

2

2 2

2 2

Signal power A 2

2AQuantization step size,

L

Quantization noise power 12

4A A

12L 3L

2

2

3Signal to quantiation noise ratio L

2Given signal to quantization noise ratio 31.8dB or 1513.56

3L 1513.56

2

L 31.76

32

15. The magnitude and phase of the complex Fourier

series coefficientsk

a of a periodic signal x(t) are

shown in the figure. Choose the correct statementform the four chices given. Notation: C is the set of

complex numbers, R is the set of purely real numbers,and P is the set purely imaginary numbers.

(A) x t R

(B) x t P

(C) x t C R

(D) The information given is not sufficient to draw

any conclusion about x(t)

Answer: (A)

Exp: k a only changes the sign of the magnitude k a . Since the magnitude spectrum k a is even the corresponding time-domain signal is real.

16. The general solution of the differential equationdy 1 cos 2y

dx 1 cos 2x

is

(A) tan y cot x c c is a constan t (B) tan x cot y c c is a constan t

k a

k 5 4 3 2 1

0 1 2 3 4

3

2 2

3

k a

k

5 4 3 2 10

1 2 3 4


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12

(C) tan y cot x c c is a constan t (D) tan x coty c c is a constan t

Answer: (C)

Exp: Givendy 1 cos 2 y

dx 1 cos 2x

dy dx

1 cos 2 y 1 cos 2x

(Variable – Separable)

2 2

2 2

dy dx

2 cos y 2 sin x

s ec ydy cosec x dx

tan y cot x k

tan y cot x k

17. An n – type silicon sample is uniformly illuminated with light which generates

20

10 electronhole pairs per cm3 per second. The minority carrier lifetime in the sample is 1 s . Int eh

steady state, the hole concentration in the sample is approximately x10 , where x is an integer.

The value of x is __________________Answer: 14

Exp: The concentration of hole-electron pair in 20 6 14 31 sec 10 10 10 cm So, the power of 10 is 14.

x 14

18. If the circuit shown has to function as a clamping circuit, which one of the following

conditions should be satisfied for sinusoidal signal of period T?

(A) RC T

Answer: (D)

19. In a source free region in vacuum, if the electrostatic potential2 2 2

2x y cz , the value ofconstant c must be __________________________

Answer: -3

C

vR


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13

Exp: 2 2 2

x y z

2x y cz

E 4xa 2ya 2cza

.E 0

4 2 2c 0

c 3

20. In an 8085 microprocessor, which one of the following instructions changes the content of theaccumulator?

(A) MOV B, M (B) PCHL (C) RNZ (D) SBI BEH

Answer: (D)

Exp: Generally arithmetic or logical instructions update the data of accumulator and flags. So, inthe given option only SBT BE H is arithmetic instruction.

SBI BEH Add the content of accumulator with immediate data BE H and store the resultin accumulator.

21. The voltage CV across the capacitor (in Volts) in the network shown is _____________

Answer: 100

Exp: 22

R c LV V V V

22 2

c

2

c

c

c

c

c

c

(100) (80) V 40

V 40 (180)(20)

V 40 2 90 20

V 40 60

V 60 40

V 60 40

V 100V

22. Let 1 2 1 2az b

f z . If f z f z for all z z ,a 2, b 4 and c 5,cz d

then d should be

equal to __________.

Answer: 10

80V 40V cV

z100V, 50 H


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14

Exp: 1 2 1 2az b

f z if f z f z , for z zcz d

1 21 2

1 2

1 2 2 1 1 2 1 2

2 1 2 1

a 2, b 4, c 5

2z 4f z

5z d2z 4 2z 4

f z f z5z d 5z d

10 z z 20 z 2dz 4d 10 z z 20 z 2dz 4d

20 z z 2d z z

d 10

23. In the circuit shown the average value of the voltageabV (in Volts) in steady state condition

is _____________.

Answer: 5

24. For the signal flow graph shown in the figure, the value of

C s

R s is

(A) 1 2 3 4

1 2 1 3 4 2 2 3 3 1 2 3 4 1 2

G G G G

1 G G H G G H G G H G G G G H H

(B) 1 2 3 4

1 2 1 3 4 2 2 3 3 1 2 3 4 1 2

G G G G


5 sin 5000t

1k 1 F 1mHa b

2k

5VabV

R s 1G 2G

1

3G

4G

2X 5X

1H 2H

3X

4X

3H

C s11X


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15

(C)1 2 1 3 4 2 2 3 3 1 2 3 4 1 2

1


(D)1 2 1 3 4 2 2 3 3 1 2 3 4 1 2

1


Answer: (B) Exp: Using mason gain formula we get it directly.

25. In the circuit shown,0 0A

V V for switch SW in position A and0 0B

V V for SW in position

B. Assume that the opamp is ideal. The value of 0B

0A

V

V is ____________________

Answer: 1.5

Exp: OB

OA

1 1k V 5 11k 1k

6V

1k 1 1k 1V 5 1 4V V V

1k 2 1k 2

OB

OA

V1.5

V

Q. No. 26 – 55 carry Two Marks Each

26. Let X 0,1 and Y 0,1 be two independent binary random variables. If P (X = 0) = p and

P(Y = 0) = q, then P X Y 1 is equal to

(A) pq 1 p 1 q (B) pq

(C) p 1 q (D) 1 pq

5V

1V

1 k

1 k

1 k

1 k

SW

1 k

0VB A


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16

Answer: (D)

Exp:

P x 0 P P x 1 1 p

P y 0 q P y 1 1 q

Let Z X Y

X Y Z0 0 0

0 1 1

1 0 1

1 1 2

From above table,

P X Y Z P Z B

P Z 1 P X 0 and Y 1 P X 1 and Y 0 P X 1 and Y 1

1 P X 0 and Y 0

1 pq

27. An LC tank circuit consists of an ideal capacitor C connected in parallel with a coil ofinductance L having an internal resistance R. The resonant frequency of the tank circuit is

(A)1

2 LC (B) 2

1 C1 R

L2 LC

(C)2

1 L1

R C2 LC

(D) 2

1 C1 R

L2 LC

Answer: (B)

Exp:

c LR

2 2 2

Y Y Y

R j L1Y j C j C

j L R R L

Placing Imaginary part to zero we get option (B).

28. n

n nX

is an independent and identically distributed (i,i,d,) random process with nX

equally likely to be n

n n1 or 1. Y

is another random process obtained as

n n n 1Y X 0.5X . The autocorrelation function of n

n nY

denoted by YR k is

L R

C


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17

(A) (B)

(C) (D)

Answer: (B)

Exp:

Y yR k R n, n k

E Y n .Y n k

Y n x n 0.5x n 1

y

X x x x

y x x

R k E x n 0.5x n 1 x n k 0.5x n k 1

E x n .x n k x n 0.5 x n k 1 0.5 x n 1 .x n k

0.25x n 1 x n k 1

E x n .x n k 0.5E x n x n k 1

0.5E x n 1 x n k

0.25E x n 1 x n k 1

R k 0.5R k 1 0.5R k 1 0.25R k

R k 1.25R k 0.5R k

x

x

1 0.5R k 1

R k E x n .x n k

2x

22

x

if k 0,

R 0 E x n

1 11 . 1

2 2

1

if k 0,

R k E x n .E x n k

0

k

YR k

3 2 1 0 1 2 3

1

k 3 2 1 0 1 2 3

1.25

0.5 0.5

YR k

2 1 0 1 2

1.25

0.5 0.5

YR k

0.25 0.25

k k 3 2 1 0 1 2 3

1.25

0.25 0.25

YR k


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18

E x n 0

E x n k 0

y x x x

y x x x

y x x x

R 0 1.25R 0 0.5R 1 0.5R 1

1.25

R 1 1.25R 1 0.5R 0 0.5R 2

0.5

R 1 1.25R 1 0.5R 2 0.5R 0

0.5

yR k for k other than 0, 1 and – 1 = 0

yR k

29. In a MOS capacitor with an oxide layer thickness of 10 nm, the maximum depletion layer

thickness is 100 nm. The permittivities of the semiconductor and the oxide layer ares ox

and

respectively. Assumings ox

/ 3, the ratio of the maximum capacitance to the minimumcapacitance of this MOS capacitor is _____________________

Answer: 4.33

Exp:

ox

max ox d max ox

ox smin ox s

ox d max

ox s

ox d max

C t X 100 11 1 4.33

C t 10 3

t X

t X

30. Let the random variable X represent the number of times a fair coin needs to be tossed till two

consecutive heads appear for the first time. The expectation of X is _____________________

Answer: 1.5

Exp: Let x be a random variable which denotes number of tosses to get two heads.

0.5 0.5

1.25

1 1 k


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19

2 3 4

1 1P x 2 HH

2 2

1 1 1P x 3 THH

2 2 2

1 1 1 1P x 4 TTHH 2 2 2 2

.........................................................

1 1 1 1 1 1 1 1 1E x 2 3 4 ..........

2 2 2 2 2 2 2 2 2

1 1 12 3 4 ...........

2 2 2

2 3

2

2

.

1 1 1 12. 3. 4 .............

2 2 2 2

1 1 11 2. 3 ...... 12 2 2

1 1 1 31 1 4 1

2 2 2 2

31. In the circuit shown, the Norton equivalent resistance in across terminals a – b is ______________.

Answer: 1.333

Exp: Nodal @ ‘a’

th th th

th

th

th

V 4I V V1 0

2 2 4

Also V 4I

4V

3

4 1R 1 1.333

3 3

4I 2 4

a

b

I

2

1A

thth

VR

1

thV42

I

4I

2

thV

b

a


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20

32. The figure shows a binary counter with synchronous clear input. With the decoding logicshown, the counter works as a

(A) mod – 2 counter (B) mod – 4 counter (C) mod – 5 counter (D) mod – 6 counter

Answer: (B)

Exp: 3 2 1 0Q Q Q Q

0 0 0 0

0 0 0 1

0 0 1 0

0 0 1 1

0 1 0 0

Once the output of Ex-NOR gate is 0 then counter will be RESET. So, Ex-NOR-gate will

produce logic 0 for Q3 = 0, Q2 = 1. So, the counter will show the sequence like:

So, it is MOD-4 counter.

33. In the ac equivalent circuit shown, the two BJTs are bbiased in active region and have

identical parameters with . The open circuit small signal voltage gain is approximately ________________________

BinaryCounter

CLK

3Q

2Q1Q

0Q

CLEAR

outv

inv

0 1 2 3


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21

Answer: -1

Exp:

When Base and collector is shorted, it act as a diode.

So0

V 0.7V.

0

in

V 0.7VGain , 1

V 0.7V

34. The state variable representation of a system is given as

0 1 1x x; x 0

0 1 0

y 0 1 x

The response y(t) is

(A) sin(t) (B) t1 e (C) 1 cos t (D) 0

Answer: (D)

Exp: X AX

1

1

X(s) sI A X(0)

s 1 1X(s) 0 s 1 0

1sX(s)

0

1x t

0

1y(t) [0 1] 0

0

35. Consider the differential equation

dx

10 0.2xdt with initial condition x 0 1 . Theresponse x t for t 0 is

(A) 0.2t2 e (B) 0.2t2 e (C) 0.2t50 49e (D) 0.2t50 49e

Answer: (C)

inV

outV


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22

Exp: Given

dxD.E 10 0.2x x 0 1

dt

dx0.2 x 10

dt

Auxiliary equation is m 0.2 0

m 0.2

Complementary solution

0.2 t

c

0tt

p

0t

0.2 t

c p

x C e

1 10ex 10 e

D 0.2 0.2

50e 50

x x x C e 50

Given

0.2 t

x 0 1 C 50 1 C 49

x 50 49 e

36. For the voltage regulator circuit shown, the input voltage inV is 20V 20% and the

regulated output volage outV is 10V. Assume the opamp to be ideal. For a load LR drawing

200 mA, the maximum power dissipation in 1Q (in Watts) is _____________.

Answer: 2.8056

Exp:1Q (max) CE (max) c max

P V I ….(i)

CE(max)V 24 10 V 14V

1

cmax

E c

R 2 R

I (200 0.4)mA

I I 200mA 0.4mA

4 0200.4mA I I mA

10

Put values in Equation (1), we get

1

3

Q (max)P 14 200.4 10 Watt

2.8056 Watt

37. Input x(t) and output y(t) of an LTI system are related by the differential equation y" t y ' t 6y t x t . If the system is neither causal nor stable, the impulse response

h(t) of the system is

(A) 3t 2t1 1

e u t e u t5 5

(B) 3t 2t1 1

e u t e u t5 5

1Q

1R LR

outVinV

ref V

2R 10k

4Vref V


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23

(C) 3t 2t1 1

e u t e u t5 5

(D) 3t 2t1 1

e u t e u t5 5

Answer: (B)

Exp: The given differential equation is,

y" t y ' t 6y t x t

On applying Laplace transform on both sides,

2s y s sy 0 y 0 s y s y 0 6y s x s

To calculate the transfer function all initial conditions are taken as ‘0’.

2

2

s s 6 y s x s

1 1 1 1 1H s

s 3 s 2 5 s 3 s 2s s 6

It is given that h(t) is non-casual and un-stable.

To satisfy both the conditions ROC should be left of the left most pole.

Using the following standard pair

at

at

1e u t ; a

s a

1e u t ; a

s a

3t 2t

3t 2t

1 1 1H s

5 s 3 s 2

1e u t e u t

5

1 1e u t e u t

5 5

So option (B) is correct.


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24

38. The diode in the circuit given below hasONV 0.7V but is ideal otherwise. The current (in

mA) in the 4k resistor is __________.

Answer: 0.6

Exp:

Bridge is Balanced., I = 0.

So,

x

1mA 9k I 0.6mA

9k 6k

2 k

4k

D

3k

6k

1mA

1k

2 k

4 k

xI

3 k

6 k

1 mA

1mA

2 k 3 k

4 k 6 k

D

1 k

I


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25

39. A zero mean white Gaussian noise having power spectral density 0 N

2is passed through an

LTI filter whose impulse response h(t) is shown in the figure. The variance of the filterednoise at t = 4 is

(A) 2 03

A N2

(B) 2 03

A N4

(C) 2 0A N (D)2

0

1A N

2

Answer: (A)

Exp: Let N(t) be the noise at the output of filter.

Variance of 22 N t E N t E N 1

Since the input noise is zero mean,

Output noise mean is also zero.

E N t E W t . h t dt

E W t 0

W t is white noise

2

N

var N t E N t

R 0

Since

N

o N

o

N

o N

R h * h * R

NSince R .

2

N

R h * h . 2

NR h k .h k dk

2

2 2 2o o N o N N 3

R 0 h k dk 3A .A .N2 2 2

0

A

1 2 3

h t

A

t


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26

40. Assuming that the opamp in the circuit shown below is ideal, the output voltage0

V (in volts)

is ___________________

Answer: 12

Exp: V V

o satSo V V 12 Volts

41. A 1 – to – 8 demultiplexer with data inputinD , address inputs 0 1 2 0S ,S ,S (with S as the LSB)

and0 7

Y to Y as the eight demultiplexed output, is to be designed using two 2 – to – 4 decoders

(with enable input E and address input 0 1A and A ) as shown in the figure in 0 1 2D , S ,S and S

are to be connected to P, Q, R and S, but not necessarily in this order. The respective input

connections to P, Q, R and S terminals should be

(A)2 in 0 1S , D , S , S (B) 1 in 0 2S ,D ,S ,S (C) in 0 1 2D ,S ,S ,S (D) in 2 0 1D ,S ,S ,S

Answer: (D)

Exp: We need to implement 1 : 8 DEMUX

Select lines of DEMUX should be mappedto address lines of decoder. So, LSB ofDEMUX should be connected to LSB ofaddress lines of decoder.

0

1

R S

S S

Input to both the decoder should be same so

inP D

NOT gate along with OR gate in case to

select one decoder at a time so aQ S .

2k

1k

1V

12V

12V

oV

1E

01A

11A

2 t o 4Decoder

o1Y

11Y

21Y

31Y

oY

1Y

2Y

3Y

02A

12A 7

2 t o 4Decoder

o2Y

12Y

22Y

32Y

4Y

5Y

6Y

7Y

P

Q

R

S

2S 1S 0S

7Y

1Y

0Y

inD


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27

in

2

0

1

P D

Q S

R S

S S

42. The value of the integral sin 4 t

12cos 2 t4 t

dt is ______________________Answer: 3

Exp:

0

0 0

t t

0 0

sin 4 t12 cos 2 t dt

4 t

12 2 cos 2 t sin 4 tdt

4 t

3 sin 6 t dt sin 2 t dtsin A cos B sin A B sin A B

t t

3 6sin 6 t sin 2 te dt e dt

t t

2 2 2 2s s

1 1

s

3 sin 6 t sin 2 tL L with s 0

t t

3 6 2ds ds with s 0

s 36 s 4

3 1 s 1 s6 . tan 2 . tan with s 0

6 6 2 2

1 1 1 1

1 1

3 s stan tan tan tan

6 2

3tan 0 tan 0

2 2

3 30 0 3

2 2

43. A function of Boolean variables X, Y and Z is expressed in terms of the min – terms as

F X, Y, Z 1, 2, 5, 6, 7

Which one of the product of sums given below is equal to the function F X,Y,Z ?

(A) X Y Z . X Y Z . X Y Z

(B) X Y Z . X Y Z . X Y Z

(C) X Y Z . X Y Z . X Y Z . X Y Z . X Y Z


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28

(D) X Y Z . X Y Z . X Y Z . X Y Z . X Y Z Answer: (B)

Exp: Given minterm is: F X,Y,Z 1,2,5,6,7

So, maxterm is :F X,Y,Z M 0,3,4

POS X Y Z X Y Z X Y Z

44. The transfer function of a mass – spring damper system is given by

2

1G s

Ms Bs K

The frequency response data for the system are given in the following table.

in rad/s G j in dB arg G j in deg

0.01 – 18.5 – 0.2

0.1 – 18.5 – 1.3

0.2 – 18.4 – 2.6

1 – 16 – 16.9

2 – 11.4 – 89.4

3 – 21.5 – 151

5 – 32.8 – 167

10 – 45.3 – 174.5

The unit step response of the system approaches a steady state value of ________________

Answer: 0.12

Exp:

Y(s) = G(s) U(s)

2

2s 0 s 0

1 1Y s .

sMs Bs K

1y limsY s lim

Ms Bs K

1y

K

Now, @ 0.01rad s, dB

G j 18.5

20log G j 18.5

U s Y s G s


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29

18.5

20

120log 18.5

k

1 18.5log

k 20

1y 10 0.1188k

y 0.12

45. Two half – wave dipole antennas placed as shown in the figure are excited with sinusoidally

varying currents of frequency 3 MHz and phase shift of / 2 between them (the element atthe origin leads in phase). If the maximum radiated E – field at the point P in the x – y plane

occurs at an azimuthal angle of o.60 the distance d (in meters) between the antennas is

_______________.

Answer: 50

Exp: = δ+βdcosθ

For maximum field, = 08

6

3 10

3 10

100m

δ+βdcosθ = 0

2d cos 60 0

2

2 1d

2 100 2

d 50m

46. An air – filled rectangular waveguide of internal dimensions a cm bcm a b has a cutoff

frequency of 6 GHz for the dominant 10TE mode. For the same waveguide, if the cutoff

frequency of the 11TM mode is 15 GHz, the cutoff frequency of the 01TE mode in GHz is

_____________.

Answer: 13.7

Exp:

OP d

y

60

x

dO

z


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30

10

c

2 2

c

11

89

2 2

TE

f 6GHz

1 m nf

a b2

1a

40

TM

3 10 1 115 10

2 a b

191.65

b

01

8

c

c

TE

3 10 1f .

2 b

f 13.7 GHz

47. Consider two real sequences with time – origin marked by the bold value

1 2x n 1, 2,3, 0 , x n 1, 3, 2,1

Let 1 2X k and X k be 4 – point DFTs of 1 2x n and x n , respectively

Another sequence 3x n is derived by taking 4 – point inverse DFT of 3 1 2x k x k x k .

The value of 3x 2 is__________

Answer: 11

Exp:

1 2

3 1 2

x n 1, 2, 3, 0 , x n 1,3, 2,1

X k X k X k

Based on the properties of DFT,

1 2 1 2 3x n x n X k X k x n

Circular convolution between two 4-point signals is as follows:

3

1 0 3 2 1 9

2 1 0 3 3 8

3 2 1 0 2 11

0 3 2 1 1 14

x 2 11

48. Let 4tx t a s t s t with s t e u t , where u t is unit step function. If the bilateral Lapalce transform of x(t) is

2

16X s 4 Re s 4

s 16

Then the value of is __________.


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31

Answer: -2

Exp:

4t

4t 4t

L4t

L4t

x t s t s t & s t e u t

x t e u t e u t

e u ts 4

e u ts 4

2 2

BX s

s 4 s 4

s 4 s 4 16; 4 4

s 16 s 16

On solving the numerator

2

49. Consider a binary, digital communication system which used pulses g t and g t fortransmitting bits over an AWGN channel. If the receiver uses a matched filter, which one of

the following pulses will give the minimum probability of bit error?

(A) (B)

(C) (D)

Answer: (A)

Exp: Optimum receiver for AWGN channel is given by matched filter.

In case of matched filter receiver,

0 1 t

g t

1

0 1 t

g t

1

0 1 t

g t

1

0 1 t

g t

1


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32

Probability of erroru

2EQ

N

Probability of error is minimum for which E is maximum.

Now looking at options

Energy in option 2A 1 1

Energy in option (C) and (D) is same = 1/3

Energy in option (B) 1 2

2

0

1 2

2

0

1 23

0

2 2t dt

2 4t dt

t2.4

3

1 3

Thus option (A) is correct answer.

50. The electric field of a plane wave propagating in a lossless non – magnetic medium is given bythe following expression

9 9x yE z, t a 5cos 2 10 t z a 3cos 2 10 t z2

The type of the polarization is

(A) Right Hand Circular. (B) Left Hand Elliptical

(C) Right Hand Elliptical (D) Linear

Answer: (B)

Exp: x

y

E 5cos t z

E 3cos t z2

2

But the wave is propagating along negative z-direction

So, Left hand elliptical (LED).


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33

51. The energy band diagram and electron density profile n(x) in a semiconductor are shown in

the figure. Assume that 3q x cm

15 kTn x 10 e , with 0.1V / cm

and x expressed in cm.

Gvien 2 1n

kT D kT0.026V, D 36cm s , and

q q

. The electron current density 2in A / cm

at x = 0 is

(A) 24.4 10 (B) 22.2 10 (C) 0 (D) 22.2 10

Answer: (C)

Exp: n ndn(x)

J (diff ) qDdx

Givenq x

15 kT

15 4

x 0

2 2

n

n(x) 10 e

dn(x)3.846 10 cm

dx

J (diff) 2.2 10 A / cm

n (drift ) n xx 0

15 19

x

x

12 2

n

J n(0).q E

10 1.6 10 1384.5 E

kT 1 dn(x)E . . 0.1V / cm

q n(x) dx

J (drift ) 2.2 10 A / cm

2

n nJ J (drift ) J (drift ) 0 A / cm

Slope 0.1eV/cm

Ec

Ev

E eV

x 0 x

log n x

x 0 x


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34

52. A dc voltage of 10V is applied across an n – type silicon bar having a rectangular cross – section

and a length of 1cm as shown in figure. The donor doping concentrationD N and the mobility

of electrons 16 3 2 1 1n are 10 cm and 1000cm V s

, respectively. The average time in s taken by the electrons to move from one end of the bar to other end is _______________.

Answer: 100

Exp:V 10

10 V md 1

4d

d 4 2d

v 1000 10 10 cm s

L L 1 100v T 100 s

T V 10 10

53. In the circuit shown, the initial voltages across the capacitors1 2

C and C are 1V and 3V,

respectively. The switch is closed at time t = 0. The total energy dissipated (in Joules) in theresistor R until steady state is reached is ________________________

Answer: 1.5

Exp:

3 1

s sI(s)

1 310

3s 3s

2 2I(s) 4 4

10s 10 s3 30

1C 3F 2C 1F

R 10 t 0

n Si

10V

1cm

1

s

3

s

1

3s

1

s

I(s)

20


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35

4t

30

2

R 0

4t

15

0

4t

15

0

1i(t) e ; t 0

5

E i (t)10dt

10e dt

25

10 e.

425

15

10 150

25 4

1.5 J

54. The output of a standard second – order system for a unit step input is given as

t2

y t 1 e cos 3t63

. The transfer function of the system is

(A)

2

s 2 s 3 (B)

2

1

s 2s 1 (C)

2

3

s 2s 3 (D)

2

4

s 2s 4

Answer: (D)

Exp: Here n

2

n

1

31

2

12

2

55. If C denotes the counterclockwise unit circle, the value of the contour integral

C

1Re z dz

2 j is _____________.

Answer: 0.5

Exp: e

1Re z dz

2 J where C is z 1


36/36


j j

2

j j

0

2

0

2 22

0 0

Put z e d je d

1Re e je d

2 j

1cos . j cos jsin d

2 j

jcos d cos sin d

2 j

j 10

2 j 2

Documents

EC GATE 15 Paper 02 New2